The quadratic equation whose sum of the roots is 11 and sum of squares of the roots is 61 is

Question

Aicharya · Accepted Answer

Let $\alpha$ and $\beta$ are roots of quadratic equation $	herefore \alpha+\beta=11$ and $\alpha^2+\beta^2=61$ $\Rightarrow(\alpha+\beta)^2-2 \alpha \beta=61$ $\Rightarrow 121-2 \alpha \beta=61 \Rightarrow \alpha \beta=30$ $	herefore$ Quadratic equation is $\begin{aligned} & \mathrm{x}^2-(\alpha+\beta) \mathrm{x}+\alpha \beta=0 \ & \mathrm{x}^2-11 \mathrm{x}+30=0\end{aligned}$

The quadratic equation whose sum of the roots is 11 and sum of squares of the roots is 61 is

Solution